Communication management system, communication system, computer-readable recording medium, and maintenance system

A communication management system includes: a storage unit configured to store destination information of a first communication terminal that establishes a first session with a relay device that relays communication data, destination information of a conversion system that performs mutual conversion between communication schemes of communication data transmitted from the first communication terminal and a second communication terminal and establishes a second session with the relay device, and destination information of the second communication terminal that establishes a third session with the conversion system; a receiving unit configured to receive start request information to start communication between the communication terminals from the first communication terminal; an extracting unit configured to extract destination information of each communication terminal and the conversion system stored in the storage unit, based on the received start request information; and a transmitting unit configured to transmit the extracted destination information to the relay device.